### E-PFRP N. 21 2016

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NOTE ON THE POWER OF PANEL COINTEGRATION TESTS

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APPLICATION TO HEALTH CARE EXPENDITURE AND

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Giorgia Marini

Università di Roma

Dipartimento di Studi Giuridici, Filosofici ed Economici

Email:

Si prega di citare così: Giorgia Marini (2016), “A note on the power of panel cointegration tests – An application to health care expenditure and GDP”, Public Finance Research Papers, Istituto di Economia e Finanza, DIGEF, Sapienza University of Rome, n. 21 (http://www.digef.uniroma1.it/ricerca).

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## Giorgia Marini

A note on the power of panel cointegration tests – An

application to health care expenditure and GDP

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### Abstract

This paper enlarges on Gutierrez's (2003) results on the power of panel cointegration tests. By a
comparison of power of panel cointegration tests, we show how the choice of most powerful test
depends on the values of the sample statistics. Country-by-country and panel stationarity and
cointegration tests are performed on a panel of 20 OECD countries over the period 1971-2004.
Residual-based tests and a cointegration rank test in the system of health care expenditure and GDP
are used to test cointegration. Asymptotic normal distribution of these tests allows a straightforward
comparison: for some values of the sample statistics, residual-based and rank tests are not directly
comparable as the power of the residual-based tests oscillates; for other values of the sample statistics,
the rank test is more powerful than the residual-based tests. This suggests that a clear-cut conclusion
*on the most powerful test cannot be reached a priori. *

**JEL classification: C12; C22; C23; I10 **

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1.

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## NTRODUCTION

Since Newhouse (1977) seminal paper, research interest has shifted from identifying the proper
determinants of health care expenditure (among others, Gerdtham, 1992; Hitiris and Posnett, 1992;
*Barros, 1998; Gerdtham et al., 1998; Roberts, 2000), to checking whether health care is a luxury good *
(among others, Blomqvist and Carter, 1997; Getzen, 2000; Freeman, 2003; Sen, 2005; Barros, 1998;
*Roberts, 2000; Giannoni and Hitiris, 2002; Di Matteo, 2003; Clemente et al., 2004; Yavuz et al., 2013), *
and more recently to solving the issue of cointegration between health care expenditure and GDP
(among others, Hansen and King, 1996; Hitiris, 1997; Gerdtham and Löthgren, 2000; Roberts, 2000;
*Gerdtham and Löthgren, 2002; Gutierrez, 2003; Jewell et al., 2003; Westerlund, 2007; Baltagi and *
*Moscone, 2010; Odubunmi et al., 2012; Payne et al., 2015). *

The main reason for this change of interests is the extended use of panel data starting from the 1990s (among others, Gerdtham, 1992; Hitiris and Posnett, 1992; Hitiris, 1997). Advantages and concerns relative to the use of panel data are discussed in various papers (among others, Banerjee, 1999; Gerdtham and Löthgren, 2002). One of the main issues raised by the use of panel data is the problem of cointegration of non-stationary variables. Various papers have tried to solve such issue but have reached inconclusive evidence on the matter both on country-by-country and panel tests (see for some examples, Hansen and King, 1996; Blomqvist and Carter, 1997; McCoskey and Selden, 1998; Gerdtham and Löthgren, 2000).

The main goal of this paper is to show how the choice of most powerful test actually depends on the empirical values of the statistics. In order to that, we proceed as follows. We first verify the existence of a cointegrating vector of non-stationary health care expenditure and GDP and then we compare the power of three panel cointegration tests to assess which is the most powerful.

Country-by-country and panel stationarity tests and country-by-country and panel cointegration tests are performed on a panel of 20 OECD countries over the period 1971-2004. Residual-based tests and a cointegration rank test in the system of health care expenditure and GDP are used to test cointegration. Asymptotic normal distribution of these tests allows a straightforward comparison. For some values of the sample statistics, residual-based tests and the cointegration rank test are not directly comparable as the power of the residual-based tests oscillates; for other values of the sample statistics, the residual-based tests and the cointegration rank test are directly comparable and the rank test is more powerful than the residual-based tests.

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## ATA DESCRIPTION

Health care expenditure (HE) and GDP are measured in national currencies and expressed in 2000
prices (deflated by GDP deflator). Both variables are taken from the OECD Health Dataset (OECD,
2006). The starting dataset contains a list of 30 OECD countries with annual data covering the period
1960-2005. Due to missing data, Czech Republic, France, Greece, Hungary, Italy, Korea, Mexico, Poland,
Slovak Republic and Turkey have been excluded and the remaining unbalanced panel dataset has a
*total of N = 20 countries. The total number of observations is T = 34 years. Both variables are *
expressed in logarithm and per capita.

As graphical analysis for HE and GDP shows that both series contain a linear trend,1_{ this characteristic }
is incorporated both into the model specification and into the tests. Description of the model
specification and tests is provided in various papers (see among others, Banerjee, 1999; Pedroni, 1999;
*Kao, 1999; Hadri, 2000; Gerdtham and Löthgren, 2000; Larsson et al., 2001; Levin et al., 2002; *

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*Gerdtham and Löthgren, 2002; Im et al., 2003; Pedroni, 2004). Therefore, only results for unit root, *
stationary and cointegration tests are presented.

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## ESULTS ON STATIONARITY AND COINTEGRATION TESTS

Results for country-by-country unit root test (labelled ADF test) and panel unit root test (labelled IPS
*test by Im et al., 2003) are presented in Table 1. *

For HE the unit root hypothesis is only rejected for Germany and Portugal on the 1%, 5% and 10%
level, for Australia and Switzerland on the 5% and 10% level, and for Belgium on the 10% level. For
GDP the unit root hypothesis can be rejected for three countries (Austria, Belgium and USA) on the 5%
and 10% level, and for three countries (Denmark, Finland and Switzerland) on the 10% level. The
*panel results fail to reject the I(1) hypothesis for both HE and GDP. *

In order to check for possible multicollinearity, a country-by-country stationarity test (labelled KPSS
*test by Kwiatkowski et al., 1992) and a panel stationarity test (labelled Hadri test by Hadri, 2000) are *
also performed and reported in Table 2.

For HE the stationarity hypothesis is rejected for six countries (Australia, Austria, Luxembourg, Portugal, Spain, and Switzerland) on the 1%, 5% and 10% level, for five countries (Canada, Denmark, the Netherlands, Sweden and UK) on the 1% and 5% level, and for the rest on the 1% level. For GDP the stationarity hypothesis cannot be rejected for Ireland, while it is rejected for nine countries (Belgium, Canada, Denmark, Finland, Portugal, Sweden, Switzerland, UK and USA) on the 1%, 5% and 10% level, for four countries (Luxembourg, New Zealand, Norway, and Spain) on the 1% and 5% level, and for the rest on the 1% level. The panel results reject the hypothesis of stationary series for both HE and GDP.

Results relative to country-by-country tests of no cointegration and panel tests of no cointegration
*(labelled Engle-Granger procedure and IPS test for homogeneous panels and LLC test by Levin et al., *
2002 for heterogeneous panels, respectively) and country-by-country tests of cointegration and panel
tests of cointegration (Phillips and Ouliaris test byPhillips and Ouliaris, 1990and LLL test by Larsson

*et al., 2001, respectively) are presented in Tables 3 and 4, respectively.*2

From Table 3, the hypothesis of no cointegration is rejected for ten countries on the 1%, 5% and 10% level, for USA on the 1% and 5% level, and for nine countries on the 1% level. The panel results fail to reject the no cointegration hypothesis.

From Table 4, the hypothesis of cointegration cannot be rejected for all countries except Denmark,
Japan, New Zealand and Sweden. The cointegrating rank is determined by the sequential likelihood
*ratio trace test procedure. Using tests at the 5% level, a rank r = 1 is found for 16 countries, indicating *
*that HE and GDP are cointegrated. For the remaining four countries the selected rank is r = 0, which *
indicate that HE and GDP are not cointegrated for these countries. For the panel rank test the
*hypothesis that the largest rank in the panel is r = 0 is rejected, but the hypothesis of a largest rank r = *

*1 cannot be rejected. *

According to the results in Tables 3 and 4, HE and GDP are cointegrated around linear trends for the sample of OECD countries.

2 *We chose the IPS test by Im et al. (2003) and the LLC test by Levin et al. (2002) instead of more *
recent test by Westerlund (2007) because both IPS and LLC tests are constructed as the panel ECM test
statistics by pooling across the

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## OWER OF THE PANEL TESTS OF COINTEGRATION

We assume that the estimated values of the three panel tests of cointegration reported at the bottom of Table 3 and 4 (IPS, LLC and LLL tests) are the true values of the statistics associated to the data generating process (DGP). The fact that all tests are normally distributed allows comparisons.

We use the sampsi STATA command to draw the power function of the three tests. This command
estimates the required power of a test comparing the characteristics of the DGP and the sample.
Therefore, for each panel test of cointegration sampsi command tests whether the value of the
sample statistics is equal to the value of the statistics associated to the DGP, given the level of
significance of the test (α* = 0.05), the size of the population and sample, and the standard deviation. *

When the value of the sample statistics is equal to the value of the statistics associated to the DGP, the test has the minimum power of 0.05. For values of the sample statistics different from the value of the statistics associated to the DGP, power of the test increases up to maximum power of 1.

Power of the three tests is represented in Figure 1. The sample statistics takes values between -8.1 and
2.5. Panel tests are directly comparable only for certain values of the statistics. For values between -7.3
and -5.1 the residual-based tests and and the rank test are not directly comparable as the power of
residual-based tests oscillates. For values between -7.3 and -6.1, the IPS test is more powerful than the
*LLC test, and vice versa for values between -6.1 and -5.1. Over the interval -5.0 and -3.75, power is not *
defined, while between -3.75 and -3 only the residual-based IPS test and the rank LLL test are directly
comparable: the latter is more powerful than the former.

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## ONCLUSIONS

This paper offers an alternative way to compare power of panel tests of cointegration based on the
comparison between values of the sample statistics and statistics associated to the DGP. The choice of
the most powerful test depends on the values of the sample statistics. Both residual-based tests and a
cointegration rank test are asymptotically normally distributed, which allows a straightforward
comparison. For some values of the statistics, the residual-based LLC test is more powerful than the
*IPS test, and vice versa for other values. For those value of the statistics such that residual-based test *
and the rank test are comparable, LLL test is more powerful than residual-based LLC test. Therefore,
the choice of the most powerful test is not only an empirical matter but also an open issue without a
clear-cut choice.

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Banerjee A. 1999. Panel data unit roots tests and cointegration: an overview. Oxford Bulletin of Economics and Statistics 61, pp. 607-629.

Blomqvist G, Carter RAL. 1997. Is health care really a luxury? Journal of Health Economics 16, pp. 207-229.

Di Matteo L. 2003. The income elasticity of health care spending. The European Journal of Health Economics 4, pp. 20-29.

Freeman DG. 2003. Is health care a necessity or a luxury? Pooled estimates of income elasticity from US state-level data. Applied Economics 35, pp. 495-502.

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Gerdtham UG, Löthgren M. 2000. On stationary and cointegration of international health expenditure and GDP. Journal of Health Economics 19, pp. 461-475.

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Getzen TE. 2000. Health care is an individual necessity and a national luxury: applying multilevel decision models to the analysis of health care expenditures. Journal of Health Economics 19, pp. 259-270.

Gutierrez L. 2003. On the power of panel cointegration tests: a Monte Carlo comparison. Economics Letters 80, pp. 105-111.

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Hansen P, King A. 1996. The determinants of health care expenditure: a cointegration approach. Journal of Health Economics 15, pp. 127-137.

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Hitiris T, Posnett J. 1992. The determinants and effects of health care expenditure in developed countries. Journal of Health Economics 11, pp. 173-181.

Im KS, Pesaran MH, Shin Y. 2003. Testing for unit roots in heterogeneous panels. Journal of Econometrics 115, pp. 53-74.

Jewell T, Lee J, Tieslau M, Strazicich MC. 2003. Stationarity of health expenditures and GDP: evidence from panel unit root tests with heterogeneous structural breaks. Journal of Health Economics 22, pp. 313-323.

Johansen S. 1991. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, pp. 1551-1580.

Johansen S. 1995. Likelihood-based inference in cointegrated vector autoregressive models. Oxford: Oxford University Press.

Kao C. 1999. Spurious regression and residual-based tests for cointegration in panel data. Journal of Econometrics 90, pp. 1-44.

Kwiatkowski D, Phillps PCB, Schmitd P, Shin Y. 1992. Testing the null hypothesis of stationary against the alternative of a unit roots. Journal of Econometrics 54, pp. 159-178.

Larsson R, Lyhagen J, Lothgren M. 2001. Likelihood-based cointegration tests in heterogeneous panels. Econometric Journal 4, pp. 109-142.

Levin A, Lin CF, Chu CSJ. 2002. Unit roots tests in panel data: asymptotic and finite sample properties. Journal of Econometrics 108, pp. 1-24.

McCoskey S.K, Selden T.M. 1998. Health care expenditure and GDP: panel data unit roots test results. Journal of Health Economics 17, pp. 369-376.

9 Newhouse JP. 1977. Medical care expenditure: a cross-national survey. Journal of Human Resources 12, pp. 115-125.

OECD. 2006. OECD Health Data: A comparative analysis of 30 countries. Paris: Credes.

Odubunmi AS, Saka JO, Oke DM. 2012. Testing the cointegrating relationship between health care expenditure and economic growth in Nigeria. International Journal of Economics and Finance 4, pp. 99-107.

Payne JE, Anderson S, Lee J, Cho MH. 2015. Do per capita health care expenditures converge among OECD countries? Evidence from unit root tests with level and trend-shifts. Applied Economics 47, pp. 5600-5613.

Pedroni P. 1999. Critical values for cointegration tests in heterogeneous panels with multiple regressors. Oxford Bulletin of Economics and Statistics 61, pp. 653-670.

Pedroni P. 2004. Panel cointegration: Asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis. Econometric Theory 20, pp. 597-625

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Westerlund J. 2007. Testing for error correction in panel data. Oxford Bulletin of Economics and Statistics 69, pp. 709-748.

10 Table 1. Country-by-country and panel unit root tests.

### HE GDP

Lags ADF Lags ADF

Australia 1 -3.772 0 -1.908 Austria 0 -2.079 0 -3.913 Belgium 0 -3.564 0 -4.109 Canada 1 -2.343 1 -2.966 Denmark 0 -2.246 0 -2.624 Finland 1 -1.957 1 -3.259 Germany 0 -4.327 0 -3.534 Iceland 1 -2.127 1 -2.562 Ireland 1 -1.231 2 -1.589 Japan 1 -2.016 1 -1.031 Luxembourg 2 -2.171 1 -2.278 Netherlands 1 -2.21 1 -2.514 New Zealand 1 -2.123 1 -2.115 Norway 1 -3.136 1 -3.078 Portugal 1 -4.558 1 -3.096 Spain 1 -2.395 1 -3.054 Sweden 1 -2.119 1 -2.736 Switzerland 1 -4.093 1 -3.394 UK 1 -2.103 1 -3.174 USA 1 -1.79 1 -4.273

IPS panel test -0.312 -1.548

Note: The maximum lag order for the ADF test (8 lags) is by default calculated from the sample size, using a rule provided by Schwert (1989). The 1%, 5% and 10% critical values are -4.316, -3.572 and -3.223 for the country-by-country test and -2.326, -1.645 and -1.282 for the panel test.

11 Table 2. Country-by-country and panel stationary tests.

HCE GDP KPSS KPSS Australia 0.101 0.188 Austria 0.079 0.147 Belgium 0.157 0.092 Canada 0.144 0.090 Denmark 0.125 0.112 Finland 0.195 0.103 Germany 0.164 0.173 Iceland 0.178 0.161 Ireland 0.160 0.225 Japan 0.194 0.195 Luxembourg 0.085 0.146 Netherlands 0.132 0.148 New 0.161 0.135 New Zealand 0.157 0.132 Portugal 0.097 0.091 Spain 0.065 0.142 Sweden 0.129 0.072 Switzerland 0.114 0.083 UK 0.127 0.113 USA 0.173 0.041

Hadri panel test 11.442 13.621

Note: Since the KPSS test has approximately correct
*size except when T is small and l is large (from *
*Kwiatkowski et al., 1992, p.170), we exclude the case *

*l = 9. Following Gerdtham and Lothgren (2000), we *

*set lag length l equal to integer[4(T/100)*1/4_{]. The }
1%, 5% and 10% critical values are 0.216, 0.146 and
0.119 for the countrybycountry test and 2.326,
-1.645 and -1.282 for the Hadri (2000) test. Serial
dependence in the disturbances is taken into account
in the Hadri (2000) test using a Newey-West
estimator of the long run variance.

12 Table 3. Country-by-country and panel tests of no cointegration.

Lags Engle-Granger procedure Australia 1 -4.137 Austria 0 -2.155 Belgium 0 -2.647 Canada 1 -3.009 Denmark 0 -2.494 Finland 1 -3.012 Germany 0 -4.052 Iceland 0 -3.585 Ireland 1 -2.925 Japan 1 -2.354 Luxembourg 0 -1.829 Netherlands 1 -3.513 New Zealand 1 -2.907 Norway 0 -4.18 Portugal 0 -3.616 Spain 2 -3.888 Sweden 1 -2.321 Switzerland 1 -3.885 UK 1 -3.819 USA 1 -3.372

IPS test for homogeneous panels -5.422

LLC test for heterogeneous panels -6.637

Note: The 1%, 5% and 10% critical values are -4.150, -3.500 and -3.180 for the country-by-country test and -2.326, -1.645 and -1.282 for the panel tests.

13 Table 4. Country-by-country and panel tests of cointegration.

Trace statistics
*Lags * *h = 0 * *h = 1 * *Rank r *
Australia 1 25.162 0.27 1
Austria 1 51.729 1.465 1
Belgium 1 91.262 3.84 1
Canada 2 16.164 0.225 1
Denmark 1 10.171 0.068 0
Finland 1 50.055 0.79 1
Germany 1 77.617 0.316 1
Iceland 1 68.978 0.154 1
Ireland 1 52.91 0.006 1
Japan 1 88.056 5.576 0
Luxembourg 1 22.148 1.016 1
Netherlands 1 51.992 0.293 1
New Zealand 1 0.347 0.014 0
Norway 1 113.989 1.367 1
Portugal 1 65.78 0.737 1
Spain 1 28.053 0.024 1
Sweden 1 8.59 0.031 0
Switzerland 1 17.122 0.467 1
UK 3 24.41 3.508 1
USA 1 48.932 0.193 1
LLL panel test 54.604 -0.592

Note: Critical values for the trace test are tabulated in
Phillips and Ouliaris (1990) and are 15.197 and 3.962 for
*testing h = 0 and h = 1, respectively. The 1%, 5% and 10% *
critical values are for the panel tests 2.326, 1.645 and
1.282.

14 Figure 1. Power of IPS, LLC and LLL tests.

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